Ch1 Part 1 Review of Functions Domain and Range

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Dr. Abdelrahim S. Mousa
Assistant Professor of Applied Mathematics
Department of Mathematics
Faculty of Science
Birzeit University
Palestine
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Study Math Online
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د. عبد الرحيم موسى
دائرة الرياضيات
جامعة بيرزيت
فلسطين
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Calculus I - Math1411

1.1 Functions and their Graphs
1.2 Combining Functions
1.3 Trigonometric Functions

2.1 and 2.2 Rates of Change and Tangent to Curves and Limit of Functions
2.3 The Precise Definition of a Limit
2.4 One-Sided Limits
2.5 Continuity
2.6 Limits Involving Infinity and Asymptotes of Graphs

3.1 Tangents and the Derivative at a Point
3.2 The Derivative as a Function
3.3 Differentiation Rules
3.4 The Derivative as a rate of Change
3.5 Derivatives of Trigonometric Functions
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Related Rates
3.9 Linearization and Differentials

4.1 Extreme Values of Functions
4.2 Mean Value Theorem
4.3 Monotonic Functions and the First derivative Test
4.4 Concavity and Curve Sketching
4.5 Applied Optimization
4.7 Anti Derivatives

5.2 Sigma Notation and Limits of Finite Sums
5.3 The Definite Integral
5.4 The Fundamental Theorem of Calculus
5.5 Indefinite Integrals and the Substitution Method
5.6 Substitution and Area Between Curves

6.1 Volumes Using Cross-Sections
6.2 Volumes Using Cylindrical Shells
6.3 Arc Length
6.4 Areas of Surfaces of Revolution

7.1 Inverse Functions and Their Derivatives
7.2 Natural Logarithms
7.3 Exponential Functions
7.4 Exponential Change and Separable Differential Equations
7.5 Indeterminate Forms and L'Hopital's Rule
7.6 Inverse Trigonometric Functions
7.7 Hyperbolic Functions
7.8 Relative Rates of Growth

8.1 Integration by Parts
8.2 Trigonometric Integral
8.3 Trigonometric Substitutions
8.4 Integration of Rational Functions by Partial Fractions
8.7 Improper Integrals

A.7 Complex Numbers